I second Schwetty's mention that the airport itself is worth looking at - so you could do a quick trip towards the centre then come back in plenty of time and have a look round. The food court (not in the main public area, but staff will tell you how to get there) is good and cheap, by the way. If you are interested in architecture, the Changi MRT station was designed by SOM and engineered by Arup, and has a remarkable long span, low-rise bridge running through it to allow walking access between terminals. The nearby Expo station (Norman Foster design) is also unusual.
Everyone has their own favourite eating places - I liked Little India (near Bugis MRT) - but it is easy to find cheap, good food almost anywhere. You can see plenty of interesting places from stations on the 'green' MRT line that links to Changi - next stop on the line after Bugis is City Hall, from which you can drop in on plenty of good camera shops like Cathay.
Some of the MRT is elevated, so you can get a good view. The green line goes underground at Kallang and pops up again at Redhill. Just don't take your durians on the MRT or the buses, that's all.
Good luck,
Helen